Rapidity
= Rapidity
{title2=$\theta=\operatorname{artanh}v$}
{wiki}
For one spatial dimension and $c=1$, a massive particle has $v=\tanh\theta$, $E=M\cosh\theta$ and $p=M\sinh\theta$. A <Lorentz boost> adds a constant to all rapidities, so a rapidity difference is invariant. Rapidity is useful for <factorized scattering>, where two-body <S-matrices> depend only on that difference.